1. John’s (know) of mathematics left much to be desired. 2. I began to feel overwhelmed by work: I felt as if I (not to be able to) do it.

3. It can’t (rain) here now. I heard the weather forecast.

1. John's knowledge of mathematics left much to be desired.

Explanation: In this sentence, we are talking about John and his knowledge of mathematics. We want to describe John's knowledge using the verb "know". However, since we are talking about the past, we need to use the past tense of the verb "know", which is "knew". So, the correct form would be "John's knew of mathematics left much to be desired."

2. I began to feel overwhelmed by work: I felt as if I wasn't able to do it.

Explanation: In this sentence, we are talking about how I started to feel overwhelmed by work. We want to describe the feeling of not being able to do the work using the verb "to be able to". However, since we are talking about the past and expressing a negative feeling, we need to use the negative past tense form "wasn't able to". So, the correct form would be "I felt as if I wasn't able to do it."

3. It can't rain here now. I heard the weather forecast.

Explanation: In this sentence, we are talking about the present situation and expressing a negative possibility or inability for it to rain. We want to use the verb "to rain" in the negative form, which is "can't rain". The reason for using "can't" instead of "won't" or "doesn't" is because "can't" expresses the idea that it is not possible for it to rain, not that it won't or doesn't rain based on other factors. So, the correct form would be "It can't rain here now."